Cyclic Causal Model Discovery in Psychology

Inferring Causal Relations Observational Data

Kyuri Park

December 14, 2022

Network Theory in Psychology

Mental disorder is produced by direct causal interactions between symptoms that reinforce each other via feedback loops. (Borsboom & Cramer, 2013).

Inferring causality from observational data

Directed Acyclic Graph (DAG)

Directed Cyclic Graph (DCG)



Problem: Estimating a cyclic causal model is fundamentally very difficult. Relaxing the acyclicity assumption entails much of theoretical complication.

Solutions exist

Solutions exist, but…

PAG: Partial Ancestral Graph ?
PAAG: Partially-oriented MAAG ?
MAAG: Maximal Almost Ancestral Graph ?

Project goals


  1. Give an accessible overview of the algorithms
  2. Investigate the performance of each algorithm
  3. Apply to the empirical data

Example

Summary


  • Causal inference is the fundamental interest in science.

  • The underlying dynamic processes of many systems contain cycles.

  • Learning cyclic causal models from observational data is challenging.

  • Our study will showcase the cyclic causal discovery algorithms that are potentially suitable for typical psychological observational data.

References


Borsboom, D., & Cramer, A. O. J. (2013). Network analysis: An integrative approach to the structure of psychopathology. Annual Review of Clinical Psychology, 9(1), 91–121. https://doi.org/10.1146/annurev-clinpsy-050212-185608
M. Mooij, J., & Claassen, T. (2020). Constraint-based causal discovery using partial ancestral graphs in the presence of cycles. In J. Peters & D. Sontag (Eds.), Proceedings of the 36th conference on uncertainty in artificial intelligence (UAI) (Vol. 124, pp. 1159–1168). PMLR. https://proceedings.mlr.press/v124/m-mooij20a.html
Richardson, T. (1996). Discovering cyclic causal structure. Carnegie Mellon [Department of Philosophy].
Strobl, E. V. (2019). A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias. International Journal of Data Science and Analytics, 8(1), 33–56. https://doi.org/10.1007/s41060-018-0158-2

Evaluation metrics

  • Precision = \(\frac{TP} {(TP + FP)} = \frac{a}{(a + d + g)}\)
  • Recall = \(\frac{TP} {(TP + FN)} = \frac{a}{(a + b + c)}\)
  • Uncertainty rate = \(\frac{\text{Number of circle endpoints} (\circ)}{\text{Total number of possible endpoints}}\)

Simulation settings

Theoretical Complications

  • Global Markov property is no longer guaranteed.

    • Need extra restrictions on \(P\) (e.g., linearly independent error terms (\(\varepsilon\)))
  • Cyclic model is not always statistically identified (even in linear case).

    • many equivalent models !
  • Equilibrium state is necessary (All \(|\lambda| < 1\)).

Constraint-Based Algorithms

Possible Practical Application

  • Personalized psychotherapy (target symptoms)

  • Medical: effective treatment design

Follow-up

Possible combination with different types of causal discovery algorithm. \(\rightarrow\) Hybrid!

CCD+ GES (greedy equivalence search)

Thank you